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Popular >

extreme f(x)= 1/5 x^3-sqrt(x^2+1)

Solution

extreme points

f (x) = \frac{1}{5} x^{3} - x^{2} + 1

Solution

Maximum (0, - 1), Minimum \frac{- 3 + 109}{6}, \frac{( - 3 + 109 ) ^{\frac{3}{2}}}{30 6} - \frac{- 3 + 109}{6} + 1

Solution steps

f^{'} (x) = \frac{3 x ^{2}}{5} - \frac{x}{x ^{2} + 1}

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

: 0 < x < \frac{109 - 3}{6},

Increasing

: \frac{109 - 3}{6} < x < \infty

Plug

x = 0

into

\frac{1}{5} x^{3} - x^{2} + 1 : - 1

Maximum (0, - 1)

Plug

x = \frac{- 3 + 109}{6}

into

\frac{1}{5} x^{3} - x^{2} + 1 : \frac{( - 3 + 109 ) ^{\frac{3}{2}}}{30 6} - \frac{- 3 + 109}{6} + 1

Minimum \frac{- 3 + 109}{6}, \frac{( - 3 + 109 ) ^{\frac{3}{2}}}{30 6} - \frac{- 3 + 109}{6} + 1

Maximum (0, - 1), Minimum \frac{- 3 + 109}{6}, \frac{( - 3 + 109 ) ^{\frac{3}{2}}}{30 6} - \frac{- 3 + 109}{6} + 1

Graph

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Frequently Asked Questions (FAQ)

What is the extreme f(x)= 1/5 x^3-sqrt(x^2+1) ?
The extreme f(x)= 1/5 x^3-sqrt(x^2+1) is